On the design of multi-stable metastructures with rotational degrees of freedom

Buckling-induced multi-stable metastructures are rationally designed structures whose unit cells exhibit bi-stable or multi-stable configurations. Apart from achieving transitions between two stable states at the unit cell level, metastructures composed of bi-stable beams are also able to realize rotations due to the spatial arrangement of beams. In this work, the design space of the geometric parameters for metastructures exhibiting both rotational and translational motions is explored on the basis of both theoretical and experimental studies. First, numerical results demonstrate that beam thickness, height and length play key roles in determining the rotational snapping. To quantify the effects of these structural parameters, we analytically model the rotational snapping behavior of a representative element that consists of two beam units. Furthermore, we conduct a comprehensive parametric survey based on the proposed model. This study reveals that the rotational stability is highly dependent on the ratio between beam thickness and height. In order to allow for rotational stable states, this ratio should be constrained within a specific range. Finally, we validate these effects by measuring the mechanical response of 3D-printed specimens with different geometric parameters.